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Indefinite product
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Indefinite product : ウィキペディア英語版
Indefinite product
In mathematics, the indefinite product operator is the inverse operator of Q(f(x)) = \frac. It is like a discrete version of the indefinite product integral. Some authors use term discrete multiplicative integration〔N. Aliev, N. Azizi and M. Jahanshahi (2007) ("Invariant functions for discrete derivatives and their applications to solve non-homogenous linear and non-linear difference equations". )〕
Thus
:Q( \prod_x f(x) )= f(x) \, .
More explicitly, if \prod_x f(x) = F(x) \,, then
:\frac = f(x) \, .
If ''F''(''x'') is a solution of this functional equation for a given ''f''(''x''), then so is ''CF''(''x'') for any constant ''C''. Therefore each indefinite product actually represents a family of functions, differing by a multiplicative constant.
==Period rule==

If T \, is a period of function f(x)\, then
:\prod _x f(Tx)=C f(Tx)^ \,

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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